Definite Integration

Let f be a differentiable function in \(\left( {0,{\pi \over 2}} \right)\). If \(\int\limits_{\cos x}^1 {{t^2}\,f(t)dt = {{\sin }^3}x + \cos x}\), then \({1 \over {\sqrt 3 }}f'\left( {{1 \over {\sqrt 3 }}} \right)\) is equal to